1560s, "debate, discussion" (on the notion of "a mental tossing to and fro"), from French agitation, from Latin agitationem (nominative agitatio) "motion, agitation," noun of action from past-participle stem of agitare "move to and fro," frequentative of agere "to set in motion, drive forward; keep in movement" (from PIE root *ag- "to drive, draw out or forth, move").
Physical sense of "state of being shaken or moving violently" is from 1580s; meaning "state of being mentally agitated" is from 1722; that of "arousing and sustaining public attention" to some political or social cause is from 1828.